The building is the Soviet Embassy, the largest non-Arab presence in tiny Kuwait. It marks a diplomatic frontier, for it is the only Gulf country that allows the presence of the Soviets and their communist allies.

But there are growing indications that that narrow foothold may be enlarged -- as a result of both East European economic needs and a new political ''atmosphere'' among the six states of the Gulf Cooperation Council (GCC).

Some oil experts have long predicted that the Russians will eventually be forced to import oil as their own reserves run low. That possibility alarms East-bloc states. They have already noted a recent tendency of the Soviet Union to sell its oil on the free market for hard currency rather than sell it to them at preferential terms.

At the same time, the six GCC countries -- Saudi Arabia, the United Arab Emirates, Bahrain, Kuwait, Oman, and Qatar - have agreed to broaden their political horizons.

Much of the impetus has come from Kuwait. Late last year Kuwaiti ruler Sheikh Jabir Ahmad Sabah toured four East-bloc countries and returned to announce he was determined to persuade his fellow Gulf leaders that diplomatic relations must be established with the East bloc.

Shortly afterward, Soviet ambassador to Kuwait Nikolai Sikatchev, the crucial link in the initiative, said the Soviet Union was ready to establish relations with a region cut off from the East bloc for more than four decades. The ambassador stressed the relations should be based on ''mutual respect and nonintervention in each other's affairs.''

They were soothing words to the conservative, fiercely Islamic sheikhdoms suspicious of both the motives and atheism of communist countries. And equally suspicious Western diplomats in the area agree the current motive appears to be economic -- at least in the short run.

The Russians' prime entree in Kuwait has been commercial links - although the gradual build up in staff (now numbering more than 100) in fact parallels a proportionate decrease in trade, a mere .02 percent of Kuwait's massive imports, according to the latest government figures.

It is the lowest level of business any of the nine Soviet bloc countries with ties to Kuwait -- and embarrassing compared with recently arrived China's more than $100 million of sales, which makes it Kuwait's most active communist trading partner.

Recent movement by East-bloc states indicates a determination to increase the percentage of petrodollar business and investment, as the first step in a Gulf-East European rapprochement.

The UAE has emerged as the trendsetter. Trade delegations from Bulgaria, Hungary, and East Germany (and Yugoslavia, too) have visited the Emirates over the past two months with encouraging results. The president of the chamber of commerce in Dubai announced he ''welcomed'' new ties with the East bloc.

Bulgarian and Hungarian officials claim they will be opening commercial offices in the near future, while the East Germans said they expect to follow suit eventually, beginning by helping develop agriculture and fisheries businesses in the UAE.

The Kuwait press predicted last month that the UAE and the tiny island state of Bahrain would establish trade relations with Czechoslovakia ''within months.''

Western diplomats here vehemently argue that Gulf-East bloc detente, particularly Saudi-Soviet relations, are still a long way off, that speculation about relations in the near future is ''dangerous.''

But Kuwaiti Foreign Minister Sheikh Sabah Ahmad Sabah thinks otherwise: ''It is the only way, and progress is being made. We are playing a role, not pushing but persuading. We say, look, see, we've had good relations with the Soviet since independence and nothing has happened.''

Other Foreign Ministry officials contend that relations would already be established if it had not been for the Soviet invasion of Afghanistan, and that even this development is being accepted by some as a fait accompli.

A number of coincidental forces have encouraged the shift, according to Kuwaiti Minister of State Abdel Aziz Hussain:

* The formation of the GCC last year and its stated goal of strategic ''commonality'' means, he said, ''it is time to adopt similar approaches to East and West. We have agreed on a type of neutrality, and that can only be served by talking to both and relying on neither.''

* The Arab perception that the US is moving closer to the Israelis under the Reagan administration has led to a reevaluation of the benefits of such a one-sided pro-US stance.

* Any hope of success for the Saudi's eight point Middle East peace plan will , in the end, require Soviet approval and participation.

GCC Secretary-General Abdallah Bishara said in February that Gulf countries had already started a discreet dialogue om matters of mutual concern with East European countries and through embassies in Kuwait

And in January, Saudi Crown Prince Fahd said the absence of diplomatic relations did not mean lack of interest or respect for communist states.

However, diplomats and officials of the Palestine Liberation Organization, who have also been involved in relaying messages between the two sides, feel the Saudis will watch how developments shape up in other Gulf states before committing themselves to a direct dialogue.

But even that may not be too far off. Kuwaiti officials confidently claim a major change will be visible within the next year.